Prove that : `(1+sin theta - cos theta)/(1+sin theta + cos theta) = tan\ theta/2`

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan theta

Prove that : (1+sin2 theta-cos 2theta)/(sin theta+cos theta)=2sin theta

Prove that (sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/((sec theta - tan theta)).

Prove that (sin theta - 2 sin^(3) theta)/(2 cos^(3) theta - cos theta) = tan theta

(sin theta-cos theta + 1) / (sin theta + cos theta-1) = sec theta + tan theta

Prove that : (1-cos theta+i sin theta)/(1+i sin theta+cos theta)=ie^(-1)tan((theta)/(2))

Prove that: (sin theta - 2 sin^(3) theta) = (2cos^(3) theta - cos theta) tan theta .

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

Prove that :(sin5 theta-2sin3 theta+sin theta)/(cos5 theta-cos theta)=tan theta

Prove that quad (sin theta-cos theta+1)/(sin theta+cos theta-1)=(1)/(sec theta-tan theta) ,using the identity sec^(2)theta=1+tan^(2)theta